In the MIW network, \(\alpha \)  is the smoothing exponent to smooth the distribution of the weight estimates in the offline dataset, whose design is motivated by [1]}.
We fix \(\alpha \)  as \(0.5\)  on the MuJoCo datasets and as \(0.2\)  on the Maze2D and Adroit datasets.
The output of the MIW network prior to \({\tt power}(\alpha )\)  is lower bounded by \(10^{-8}\)  to avoid gradient explode.
We follow [2]} to initialize the weights of last layer of the MIW network from \(\mathrm {Uniform}\left(-0.003, 0.003\right)\) , and bias as 0.
